Renormalized Yang-Mills Energy on Poincaré-Einstein Manifolds

In this talk we prove that the renormalized Yang-Mills energy on six dimensional Poincaré-Einstein spaces can be expressed as the bulk integral of a local, pointwise conformally invariant integrand. We show that the latter agrees with the corresponding anomaly boundary integrand in the seven dimensional renormalized Yang-Mills energy. Our methods rely on a generalization of the Chang-Qing-Yang method for computing renormalized volumes of Poincaré-Einstein manifolds, as well as known scattering theory results for Schrödinger operators with short range potentials.